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arXiv:cond-mat/0104361

Quantum coherence of double-well BEC: a SU(2)-coherent-state path-integral approach

Yi Zhou, Hui Zhai, Lü, Rong, Zhan Xu, Lee Chang

Published Apr 19, 2001• 0 citations
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Abstract

Macroscopic quantum coherence of Bose gas in a double-well potential is studied based on SU(2)-coherent-state path-integral. The ground state and fluctuations around it can be obtained by this method. In this picture, one can obtain macroscopic quantum superposition states for attractive Bose gas. The coherent gap of degenerate ground states is obtained with the instanton technique. The phenomenon of macroscopic quantum self-trapping is also discussed.

DOI
10.48550/arxiv.cond-mat/0104361

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Macroscopic quantum coherence of Bose gas in a double-well potential is studied based on SU(2)-coherent-state path-integral. The ground state and fluctuations around it can be obtained by this method. In this picture, one can obtain macroscopic quantum superposition states for attractive Bose gas. The coherent gap of degenerate ground states is obtained with the instanton technique. The phenomenon of macroscopic quantum self-trapping is also discussed.
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We develop a Fock-space WKB method for a Bose-Einstein condensate (BEC) in a double-well trap, using an analogy with a single particle of either positive or negative mass in a quantum potential. The usual mean-field approach is the classical limit, and the inverse number of atoms plays the role of Planck constant. The ground state of positive-mass particles corresponds to the mean-field fixed point of lower energy, while that of negative mass to the excited fixed point. In the case of attractive BECs above the threshold for symmetry breaking, the ground state is the Schr\"odinger cat state and we relate this to the double-well shape of the potential in Fock space. In the repulsive case, we identify the quantum states corresponding to the mean-field macroscopic self-trapping phenomenon. In particular, the phase-locked ($\ensuremath{\pi}$ phase) macroscopic quantum self-trapping of BECs is related to the double-well shape of the potential in Fock space. The running-phase macroscopic quantum self-trapping state is found to be subject to quantum collapses and revivals. The phase dispersion grows exponentially, reaching the absolute maximum just before the first collapse of the running phase, which may explain the growth of the phase fluctuations seen in the experiment on macroscopic quantum self-trapping.
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We consider a Bose-Einstein condensate in a double-well potential undergoing a dynamical transition from the regime of Josephson oscillations to the regime of self-trapping. We analyze the statistical properties of the ground state (or the highest excited state) of the Hamiltonian in these two regimes for attractive (repulsive) interactions. We demonstrate that it is impossible to describe the transition within the mean-field theory. In contrast, the transition proceeds through a strongly correlated delocalized state, with large quantum fluctuations, and spontaneous breaking of the symmetry.
We study the macroscopic quantum self-trapping effect in a mixture of Bose–Einstein condensate (BEC) and quantum degenerate fermions, confined in a double-well potential with a variable separation between the wells. The fermions form a finite-size cloud that affects the static and dynamical properties of the BEC. In particular, our quasi-analytical and numerical analysis based on a mean-field model shows that the main features of macroscopic quantum self-trapping in a pure bosonic system are modified by the influence of fermions. Both the onset of self-trapping and the properties of the self-trapped state depend on the amount of fermions in the system as well as on the type of inter-species interaction. The properties of the quantum degenerate mixture are explored using realistic parameters for a 40 K– 87 Rb system.